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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Keywords: Cauchy method ; steepest descent ; convex programming ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We discuss two issues related to the Cauchy algorithm. First, we use anArmijo search with constant α≥0.5 and show that the sequence isFejer convergent to the optimal set, and hence convergent. Second, we useexact line searches and show an example in which the sequence fails toconverge.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-2878
    Keywords: Duality theory ; linear systems ; nonlinear programming ; convex programming ; distributed control systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of singular control problems involving amplitude constraints on the controls is examined. IfL ∞ is the space of control functionsU, the control constraint setS can be identified with the unit ball inL ∞. Now, for anyn ∈ (1, ∞), an analogous problem may be set up withL n forU and the unit ball inL n forS. This modified problem is necessarily nonsingular for controllable systems. It is shown that, by takingn sufficiently large, the solution to the modified problem also solves the original problem arbitrarily closely (in a sense made precise). Behavior asn → ∞ is investigated.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1573-2878
    Keywords: Engineering design ; nonlinear programming ; convex programming ; optimization theorems ; approximation of functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A possible mathematical formulation of the practical problem of computer-aided design of electrical circuits (for example) and systems and engineering designs in general, subject to tolerances onk independent parameters, is proposed. An automated scheme is suggested, starting from arbitrary initial acceptable or unacceptable designs and culminating in designs which, under reasonable restrictions, are acceptable in the worst-case sense. It is proved, in particular, that, if the region of points in the parameter space for which designs are both feasible and acceptable satisfies a certain condition (less restrictive than convexity), then no more than 2 k points, the vertices of the tolerance region, need to be considered during optimization.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1573-2878
    Keywords: Detection theory ; estimation theory ; sidelobe constraints ; convex programming ; duality theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The design of filters for detection and estimation in radar and communications systems is considered, with inequality constraints on the maximum output sidelobe levels. A constrained optimization problem in Hilbert space is formulated, incorporating the sidelobe constraints via a partial ordering of continuous functions. Generalized versions (in Hilbert space) of the Kuhn-Tucker and duality theorems allow the reduction of this problem to an unconstrained one in the dual space of regular Borel measures.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1573-2878
    Keywords: Detection theory ; estimation theory ; sidelobe constraints ; convex programming ; duality theory ; gradient methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An algorithm is presented for the design of optimal detection filters in radar and communications systems, subject to inequality constraints on the maximum output sidelobe levels. This problem was reduced in an earlier paper (Ref. 1) to an unconstrained one in the dual space of regular Borel measures, with a nondifferentiable cost functional. Here, the dual problem is solved via steepest descent, using the directional Gateaux differential. The algorithm is shown to be convergent, and numerical results are presented.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1573-2878
    Keywords: Variational inequalities ; convex programming ; complementarity problems ; exceptional families ; existence theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper introduces the concept of exceptional family for nonlinear variational inequality problems. Among other things, we show that the nonexistence of an exceptional family is a sufficient condition for the existence of a solution to variational inequalities. This sufficient condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. From the results in this paper, we believe that the concept of exceptional families of variational inequalities provides a new powerful tool for the study of the existence theory for variational inequalities.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1573-2878
    Keywords: Compartment models ; duality theory ; convex programming ; impulsive control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The optimal impulsive control of systems arising from linear compartment models for drug distribution in the human body is considered. A system of linear, time-invariant, homogeneous differential equations is given along with a set of continuous constraints on state and control. The object is to develop a constructive algorithm for the computation of the optimal control relative to a convex cost functional. Under suitable hypotheses, satisfying the continuous constraints is equivalent to satisfying the constraints at a finite set of abstractly definedcritical points. Once these critical points have been determined, the solution of the optimal control problem is found as the solution of an ordinary finite-dimensional convex programming problem. An iterative algorithm is given for the situation in which the critical points cannot all be determineda priori.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1573-2878
    Keywords: Pareto optimality ; multiobjective programming ; convex programming ; subgradient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Necessary conditions of Fritz John and Kuhn-Tucker type for Pareto optimality are derived by first reducing a vector minimization problem (multiobjective programming) to a system of scalar minimization problems and then using known results in convex programming.
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1573-2878
    Keywords: Duality theory ; nonlinear programming ; mathematical programming ; convex programming ; optimization theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Duality relations for the programming problem of a special class where the objective function is a sum of positive-semidefinite quadratic forms, and a sum of square roots of positive-semidefinite quadratic forms, over a convex polyhedral cone in complex space are considered. The duality relations between the primal problem and its dual are established.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Keywords: Decomposition methods ; convex programming ; large-scale programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Rutenberg (Ref. 1) provided a decomposition method to solve the problem of minimizing a separable, nonlinear objective function with large-scale linear constraints by using the convex simplex method (Ref. 2). However, there seem to be some errors in his paper (Ref. 3). This paper will rebuild the method by using more convenient and consistent notation.
    Type of Medium: Electronic Resource
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